Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 3840, how they are used in real life, and tips to learn them quickly.
The numbers that divide 3840 evenly are known as factors of 3840.
A factor of 3840 is a number that divides the number without a remainder.
The factors of 3840 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1280, 1920, and 3840.
Negative factors of 3840: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -128, -160, -192, -240, -320, -384, -480, -640, -960, -1280, -1920, and -3840.
Prime factors of 3840: 2, 3, and 5.
Prime factorization of 3840: 27 × 3 × 5.
The sum of factors of 3840: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 128 + 160 + 192 + 240 + 320 + 384 + 480 + 640 + 960 + 1280 + 1920 + 3840 = 10896
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 3840. Identifying the numbers which are multiplied to get the number 3840 is the multiplication method.
Step 1: Multiply 3840 by 1, 3840 × 1 = 3840.
Step 2: Check for other numbers that give 3840 after multiplying
2 × 1920 = 3840
3 × 1280 = 3840
4 × 960 = 3840
5 × 768 = 3840
6 × 640 = 3840
8 × 480 = 3840
10 × 384 = 3840
12 × 320 = 3840
15 × 256 = 3840
16 × 240 = 3840
20 × 192 = 3840
24 × 160 = 3840
30 × 128 = 3840
32 × 120 = 3840
40 × 96 = 3840
48 × 80 = 3840
60 × 64 = 3840
Therefore, the positive factor pairs of 3840 are: (1, 3840), (2, 1920), (3, 1280), (4, 960), (5, 768), (6, 640), (8, 480), (10, 384), (12, 320), (15, 256), (16, 240), (20, 192), (24, 160), (30, 128), (32, 120), (40, 96), (48, 80), (60, 64). For every positive factor, there is a negative factor.
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 3840 by 1, 3840 ÷ 1 = 3840.
Step 2: Continue dividing 3840 by the numbers until the remainder becomes 0.
3840 ÷ 1 = 3840
3840 ÷ 2 = 1920
3840 ÷ 3 = 1280
3840 ÷ 4 = 960
3840 ÷ 5 = 768
3840 ÷ 6 = 640
3840 ÷ 8 = 480
3840 ÷ 10 = 384
3840 ÷ 12 = 320
3840 ÷ 15 = 256
3840 ÷ 16 = 240
3840 ÷ 20 = 192
3840 ÷ 24 = 160
3840 ÷ 30 = 128
3840 ÷ 32 = 120
3840 ÷ 40 = 96
3840 ÷ 48 = 80
3840 ÷ 60 = 64
Therefore, the factors of 3840 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1280, 1920, 3840.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 3840 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3840 ÷ 2 = 1920
1920 ÷ 2 = 960
960 ÷ 2 = 480
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 3 = 10
10 ÷ 5 = 2
2 ÷ 2 = 1
The prime factors of 3840 are 2, 3, and 5.
The prime factorization of 3840 is: 2^7 × 3 × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3840 is divided by 2 to get 1920.
Step 2: Now divide 1920 by 2 to get 960.
Step 3: Then divide 960 by 2 to get 480.
Step 4: Divide 480 by 2 to get 240.
Step 5: Divide 240 by 2 to get 120.
Step 6: Divide 120 by 2 to get 60.
Step 7: Divide 60 by 2 to get 30.
Step 8: Divide 30 by 3 to get 10.
Step 9: Divide 10 by 5 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3840 is: 27 × 3 × 5.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 3840: (1, 3840), (2, 1920), (3, 1280), (4, 960), (5, 768), (6, 640), (8, 480), (10, 384), (12, 320), (15, 256), (16, 240), (20, 192), (24, 160), (30, 128), (32, 120), (40, 96), (48, 80), (60, 64).
Negative factor pairs of 3840: (-1, -3840), (-2, -1920), (-3, -1280), (-4, -960), (-5, -768), (-6, -640), (-8, -480), (-10, -384), (-12, -320), (-15, -256), (-16, -240), (-20, -192), (-24, -160), (-30, -128), (-32, -120), (-40, -96), (-48, -80), (-60, -64).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 3840 apples to be packed into boxes of 64 apples each. How many boxes are needed?
60 boxes are needed.
To determine the number of boxes, divide the total apples by the number of apples per box. 3840/64 = 60
A rectangular field has an area of 3840 square meters and a width of 80 meters. Find the length.
48 meters.
To find the length of the field, use the formula,
Area = length × width
3840 = length × 80
To find the value of length, divide 3840 by 80.
3840/80 = length
Length = 48.
There are 120 workers and 3840 tasks. How many tasks will each worker complete if they are distributed evenly?
Each worker will complete 32 tasks.
To find the tasks each worker will complete, divide the total tasks by the number of workers.
3840/120 = 32
A warehouse has 3840 pallets, and they need to be stored in 240 sections. How many pallets will be in each section?
16 pallets in each section.
Divide the total number of pallets by the number of sections to find how many pallets go into each section.
3840/240 = 16
A company produces 3840 units of a product. If they are packed into boxes containing 48 units each, how many boxes are required?
80 boxes are required.
Divide the total units by the number of units per box.
3840/48 = 80
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.